最大流sap

Posted 2020-10-08 DearDongchen

带当前弧优化 gap优化的sap 甚至省去了开始的bfs分层 

虽然花了一些时间了解原理 但是感觉不亏 现在能完全独立靠原理写出具体实现了

#include<cstdio>
#include<cstring>
using namespace std;
const int maxn = 1007, maxm = 10007, inf = 0x3f3f3f3f;
int st, ed, tot, n, m;
struct Edge{
    int u, v, nxt, w, f;
    Edge(){}
    Edge(int u, int v, int nxt, int w, int f):u(u), v(v), nxt(nxt), w(w), f(f){}
}edge[maxm];
int head[maxn], cur[maxn], gap[maxn], dep[maxn], pre[maxn];
void init(){
    tot = 0;
    memset(head, -1, sizeof head);
}
void addedge(int u, int v, int w){
    edge[tot] = Edge(u, v, head[u], w, 0);
    head[u] = tot++;
    edge[tot] = Edge(v, u, head[v], 0, 0);
    head[v] = tot++;
}
int sap(){
    memset(gap, 0, sizeof (gap));
    memset(dep, 0, sizeof (dep));
    memcpy(cur, head, sizeof (head));
    int u = st;
    pre[u] = -1;
    gap[0] = n;
    int ans = 0;
    while(dep[st] < n){
        if(u == ed){
            int MIN = inf;
            for(int i = pre[u]; i != -1; i = pre[edge[i].u]){
                if(MIN > edge[i].w - edge[i].f)
                    MIN = edge[i].w - edge[i].f;
            }
            for(int i = pre[u]; i != -1; i = pre[edge[i].u]){
                edge[i].f += MIN;
                edge[i^1].f -= MIN;
            }
            u = st;
            ans += MIN;
            continue;
        }
        bool flag = false;
        int v;
        for(int i = cur[u]; i != -1; i = edge[i].nxt){
            v = edge[i].v;
            if(edge[i].w - edge[i].f && dep[v]+1 == dep[u]){
                flag = true;
                cur[u] = pre[v] = i;
                break;
            }
        }
        if(flag){
            u = v;
            continue;
        }
        int MIN = n;
        for(int i = head[u]; i != -1; i = edge[i].nxt){
            if(edge[i].w - edge[i].f && dep[edge[i].v] < MIN){
                MIN = dep[edge[i].v];
                cur[u] = i;
            }
        }
        gap[dep[u]]--;
        if(!gap[dep[u]])
            return ans;
        dep[u] = MIN+1;
        gap[dep[u]]++;
        if(u != st)
            u = edge[pre[u]].u;
    }
    return ans;
}
int main(){
    int t, kase = 1;
    scanf("%d", &t);
    while(t--){
        init();
        scanf("%d%d", &n, &m);
        while(m--){
            int u, v, w;
            scanf("%d%d%d", &u, &v, &w);
            addedge(u, v, w);
        }
        st = 1, ed = n;
        printf("Case %d: ", kase++);
        printf("%d\n", sap());
    }
    return 0;
}